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A rod of mass $m$ and length $l$ is rising about a fixed point in the ceiling with an angular velocity $\omega$ as shown in the figure. figure

Now, on taking a small element on the rod, the net tension force will act along the rod upwards. Taking components of tension $T$ along vertical and horizontal: $$T = \delta{m}g\cos{\theta} $$ Therefore, as tension is providing centripetal force, $$T\sin{\theta} = \delta{m}\omega^2r $$ where $r =$ radius of the circle in which the element is rotating.

Implies: $$ \omega^2r = g \tan{\theta} $$

figure Now here's the problem, everything except $r$ is a constant, I.e $r$ depends on the element we take. How is that possible ?

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    $\begingroup$ From my presumption r is merely depending on the speed of rotation vis a vis the angle with the vertical $\endgroup$
    – Abhinav
    Nov 8, 2015 at 10:38
  • $\begingroup$ Here r is radius of any circle in which an element of rotating. For same values of $\theta $ and $\omega$, r should take different values. $\endgroup$
    – TESLA____
    Nov 8, 2015 at 14:01

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